On Tuesday, the White House backed down on its threat to veto a bill requiring congressional review of an Iran deal. The legislation was made more palatable by shortening the review period and by removing one controversial requirement.

Washington — [Updated April 15 at 9:45 a.m.] On Tuesday, senators succeeded in getting the White House to back down on its threat to veto a bill requiring congressional review of an Iran deal. They did it the way that most Americans want them to, by working out a compromise that was acceptable to both political parties and to the president.

The question in Congress was never whether lawmakers could pass a bipartisan bill that gives them a say in any final nuclear deal with Iran. Rather, the issue was how to shape such a bill so that it could sustain a promised presidential veto – or cause the White House to drop its threat.

Or both. Which is apparently what happened on Tuesday. The compromise answered some White House concerns, although Secretary of State John Kerry was arguing against the bill earlier in the day, according to the Associated Press. It was the number of Republicans and Democrats supporting the legislation that made the White House shift its stance, the AP reported.

President Obama is not “particularly thrilled” with the adjusted bill, which unanimously passed the Senate Foreign Relations Committee on Tuesday, White House spokesman Josh Earnest told reporters earlier in the day. But if it stays as is, the president would be willing to sign it, he said.

The administration's fear has been that congressional review could upend final international negotiations as they head toward a June 30 deadline. But the bill was made more palatable by shortening the review period and by removing a requirement that the White House periodically certify that Iran is not supporting terrorism (though the administration must regularly certify to Congress that Iran is living up to the terms of an agreement).

Senators point to several factors behind the compromise:

A pragmatic chairman. When Republicans took control of the Senate in January, the chairmanship of the Foreign Relations Committee went to Sen. Bob Corker (R) of Tennessee. A former mayor of Chattanooga and business owner, he is known as someone who can work across the aisle.

“He has an outcome orientation, and I think he is pragmatic and cleareyed about the implication of having a Democratic president and Republican Congress,” Sen. Chris Coons (D) of Delaware told reporters Tuesday morning.

Senator Coons, a member of the Foreign Relations Committee who worked on the compromise, described Senator Corker as “receptive” and as “a fair negotiator.”

Notably, Corker did not add his signature to a controversial letter for the government of Iran that was signed by 47 GOP senators in March. Instead, as he repeatedly told reporters, he was focused on getting a veto-proof majority for his bipartisan Iran bill, which was cosponsored by Sen. Robert Menendez (D) of New Jersey.

A key Democrat who’s more White House-friendly. That would be the new ranking member on the Foreign Relations Committee, Sen. Benjamin Cardin of Maryland. He stepped into the position after Senator Menendez was indicted April 1 in connection with an alleged bribery scheme.

Menendez has been at odds with the White House over Iran negotiations and Cuba policy. Senator Cardin, by contrast, supports Mr. Obama’s Cuba policy and was not an original co-sponsor of the Corker-Menendez bill.

Cardin consulted closely with the administration. “I’ve listened to the White House and many of their concerns,” he told reporters earlier on Tuesday.

As for Menendez, he was fully onboard with the compromise.

Lawmakers’ desire to be relevant. Republican and Democrat lawmakers have felt strongly that they should have a say on any Iran deal. True, a final agreement would not be a treaty, which would require Senate ratification. But because an Iran agreement would include lifting sanctions that Congress imposed, Congress should at least have an opportunity to approve or disapprove a deal, lawmakers have argued.

Without strong support for the bill, however, that opportunity would have been lost to a presidential veto. Thus, to remain “relevant,” lawmakers had to compromise, Coons said.

“This is an agreement that really is about nuclear war for our children and grandchildren, so the import can’t be magnified too much,” says Sen. John Boozman (R) of Arkansas. “I appreciate” that Corker and Cardin negotiated “in good faith to find some common ground with the administration.”

Next, the bill will head to the Senate floor for a vote, and if it survives possible poison-pill amendments, it will be quickly taken up by the House, which also wants its voice heard and is expected to pass it.

That would not portend congressional approval of a final Iran agreement, though. Lawmakers have many questions and doubts about the timing of sanctions relief, about technical issues, and about trusting Iran on anything.